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\title{Notes on Event-based Asychronous Sparse Convolutional Networks}
\author{dandelight\\
        \small{Sichuan University}\\
        \small \texttt{dandelight@qq.com}}

\date{March 14, 2021}


\newcommand{\usite}{\mathbf{u}}
\newcommand{\kidx}{\mathbf{k}}


\begin{document}

  \maketitle

  \section{Event-based camera\\ and its characteristics}

  \emph{Event-based cameras} are bio-inspired sensors that captures not normal pictures but
  pixel-wise brightness changes\footnote{Frequency not included?} termed \emph{events}.

  To be formal, a event camera is composed of indepencent pixels $\usite = (x_k, y_k)^T$ that respond to brightness changes $L(\usite_k, t_k)\doteq \log I(\usite_k, t_k)$. An event is triggered at pixel $\usite_k$ at time $t_k$ exactly when the brightness change reaches a threshold, $\pm C$.

  \[
    L(\usite_k, t_k) - L(\usite_k, t_k - \Delta t_k) \ge p_k C
  \]

  where $p \in \{-1, +1\}$ is the sign of brightness change and $\Delta t_k$ is the time elapesed??

  Due to its \textbf{asynchronos} and \textbf{sparse} nature, it's not possible to use
  normal\footnote{or standard, as said in this paper} machine learning algorithms without
  change.

  \section{Work}

  This work reduces the computational complexity by leaving out \emph{zero feature vectors} and ignoring inputs in the receptive field of convolution which is zero, only processing the non-zero feature vectors, \emph{active sites} $\mathcal A_t$.

  And its use of the \emph{rulebooks} is also very innovative. A rulebook $\mathcal R_{t, \kidx}$ is a datastructure that stores pairs of $\langle i, j\rangle$ \footnote{in case you forget about what receptive fields are, $r_n = r_{n-1} + (k_n - 1)\prod_{i=1}^{n-1}s_i$}

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